This video is a good demonstration of how to properly clean your ear and get rid of ear wax. Understand your ear's anatomy to better maintain your aural health.
There are some other techniques to remove earwax, notably using an ear pick (curette). This is usually used by your ear doctor to remove the earwax manually. You can buy them online, but I don't recommend them because you might accidentally perforate your eardrum if you don't know what you are doing.
There are also different kinds of earwax, notably dry type ear wax and wet type. The dry type is found in East Asian individuals like people of Chinese, or Japanese descent. The wet type is found in people of African, European, and South Asian descent (Indian). The dry type of earwax is generally easier to remove with a curette, than the wet type.
To work earwax out of your ear on its own, you can chew (masticate). Chewing helps the earwax work its way out of your ear so you can gently wipe it off with a washcloth in the bath. Chewing gum helps with this.
Warnings, and dangers
The number one thing you don't want to do is clean your ear with a Q-Tip or cotton swab. This will force more earwax deeper into your ear and impact against your eardrum. Never stick foreign objects into your ear as you can easily damage your eardrum. When using an ear syringe, always use a reasonable flow, don't overdo it and stop if you feel pain. Don't flush your ear canal with fluid if you have a hole in your eardrum! Never use ear candling. It's dangerous and it doesn't work.